重建极性连续统理论的基本定律和原理(Ⅰ)——微极连续统

基金项目: 国家自然科学基金资助项目(10072024);辽宁省教育委员会基础研究基金资助项目(990111001)

Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅰ)-Micropolar Continua

Department of Mathematics & Center for the Application of Mathematics, Liaoning University, Shenyang 110036, P.R.China

摘要: 在对现有微极连续统理论已进行过再研究的基础上重新建立较为完整的微极连续统理论的基本均衡定律和方程体系。在此重建的新体系中不但考虑了由于动量引起的附加动量矩、面力引起的附加面矩和体力引起的附加体矩,而且还考虑了微角速度引起的附加速度,从而可以建立起耦合型的动量、动量矩和能量的均衡定律。从这些新的基本均衡定律可以很自然地推导出相应的局部和非局部均衡方程。通过对比可以清楚地看到这些新结果较之现有的结果都完整。
- 微极连续统 /
- 耦合型 /
- 基本均衡定律 /
- 均衡方程
Abstract: Based on the restudies of existing polar continuum theories rather complete systems of basic balance laws and equations for micropolar continuum theory are presented.In these new systems not only the additional angular momentum,surface moment and body moment produced by the linear momentum,surface force and body force,respectively,but also the additional velocity produced by the angular velocity are considered.The new coupled balance laws of linear momentum,angular momentum and energy are reestablished.From them the new coupled local and nonlocal balance equations are naturally derived.Via contrast it can be clearly seen that the new results are believed to be rather general and complete.
- micropolar continuum /
- coupled /
- basic law /
- balance equation

[1]	戴天民.带有微结构的连续统中新的能量守恒定律和C-D不等式[J].应用数学和力学,2001,22(2):119-126.
[2]	戴天民.广义连续统场论中新的功能及功率能率原理[J].应用数学和力学,2001,22(11):1111-1118.
[3]	DAI Tian-min. New laws and principles for continuum mechanics-Part Ⅰ :Balance laws and equations [A]. In: CHIEN Wei-zang Ed. Proceedings of the 4 th International Conference on Nonlinear Mechniacs[C].Shanghai:Shanghai University Press,2002,206-209.
[4]	DAI Tian-min. On basic laws and principles for continuum field theories[A]. In:CHIEN Wei-zang Ed.Proceedings of the 4 th International Conference on Nonlinear Mechniacs [C]. Shanghai: Shanghai University Press,2002,29-41.
[5]	A C爱林根,C B卡法达.微极场论[M].戴天民译.南京:江苏科学技术出版社,1982,17-23.
[6]	Eringen A C. Microcontinuum Field Theories[M]. New York:Springer-Verlag, 1999.
[7]	Stojanovic R. On the principle of virtual work in the theory of oriented elastic media [J]. Z Angew Math Mech, 1973, 53: T79-T82.
[8]	Wang J, Dhaliwa R S. On some theorems in the nonlocal theory of micropolar elasticity [J]. Int J Solids Structures, 1993,30(10): 1331-1338.